If the marginal cost for a company is 𝑓(𝑞) = 28.3, find ∫ 28.3 𝑑𝑞, which gives the form of the cost function.

Question

If the marginal cost for a company is 𝑓(𝑞) = 28.3, find ∫ 28.3 𝑑𝑞, which gives the

form of the cost function.

Answer 1

The total cost function of any marginal cost is the anti-derivative with respect to q. In this case, if the MC = 28.3, then the anti-derivative of this function is just TC = 28.3Q. The meaning of this type of function is that each additional unit will cost the firm 28.3 to produce, which will be a constant cost of increasing production.

You can always check your work if you take the partial derivative of the new cost function and you should get the same MC function:

TC=28.3Q

MC = 28.3